GAS POWER CYCLES 651

dharm
\M-therm\Th13-3.pm5

For adiabatic compression process 1-2,

p 1 V 1 γ = p 2 V 2 γ

or p 2 = p 1. V
V

1

2

F

HG

I

KJ

γ

= 1 × (15)1.41 γ= = =

L

N

M

O

Q

P

c

c

p

v

10

071

. 141
.
.

= 45.5 bar

Also,

T

T

V

V

2

1

1

2

1

=

F

HG

I

KJ

−γ

= ()rγ−^11411 =( )^15. − = 3.04

∴ T 2 = T 1 × 3.04 = 373 × 3.04 = 1134 K or 861°C

For constant volume process 2-3,

p

T

p

T

2

2

3

3

=

or T 3 = T 2 ×

p

p

3

2

= 1134 ×

65

45 5.

= 1620 K or 1347°C

According to characteristic equation of gas,

p 1 V 1 = mRT 1

∴ m =

pV

RT

11

1

1 10^5 0 009

287 373

=

××

×

.

= 0.0084 kg (air)

Heat added during constant volume process 2-3,

= m × cv (T 3 – T 2 )

= 0.0084 × 0.71 (1620 – 1134)

= 2.898 kJ

Amount of fuel added during the constant volume process 2-3,

=

2 898

43890

.

= 0.000066 kg

Also as air-fuel ratio is 21 : 1.

∴ Total amount of fuel added =

0 0084

21

.
= 0.0004 kg
Quantity of fuel added during the process 3-4,
= 0.0004 – 0.000066 = 0.000334 kg
∴ Heat added during the constant pressure operation 3-4
= 0.000334 × 43890 = 14.66 kJ
But (0.0084 + 0.0004) cp (T 4 – T 3 ) = 14.66
or 0.0088 × 1.0 (T 4 – 1620) = 14.66

∴ T 4 = 14 66

0 0088

.

.

+ 1620 = 3286 K or 3013°C

Again for process 3-4,

V

T

V

T

3

3

4

4

= or V 4 =

VT

T

34

3

0 0006 3286

1620

=

. ×
= 0.001217 m^3
For adiabatic expansion operation 4-5,
T
T

V

V

4

5

5

4

(^1) 141 1
0 009
0 001217

F
HG
I
KJ
=FHG IKJ
γ− −
.
.
.
= 2.27